Constructive mathematics with the knowledge predicate K satisfied by
every currently known theorem
September 6, 2013
Mathematics
Number Theory
K denotes both the predicate satisfied by every currently known theorem and
the finite set of all currently known theorems. The set K is time-dependent,
publicly available, and contains theorems both from formal and constructive
mathema...
Fractal-cluster theory and thermodynamic principles of the control and
analysis for the self-organizing systems
September 5, 2013
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Physics
Adaptation and Self-Organizing Systems
Physics and Society
Adaptation and Self-Organizing Systems
Physics and Society
The theory of resource distribution in self-organizing systems on the basis
of the fractal-cluster method has been presented. In turn, the fractal-cluster
method is based on the fractal-cluster relations of V.P. Burdakov and the
analytical ...
Necessary condition for divisibility by the power of prime ideal and its
application to Fermat's Last Theorem
September 1, 2013
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Mathematics
General Mathematics
In the paper one proves a necessary condition for divisibility of integral
elements by the powers of prime divisor of unramifed prime ideal and gives its
application to a simple proof of Fermat's Last Theorem....
A note on the random greedy independent set algorithm
August 16, 2013
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Mathematics
Combinatorics
Let r be a fixed constant and let H be an r-uniform, D-regular hypergraph on
N vertices. Assume further that D > N^\epsilon for some \epsilon>0. Consider
the random greedy algorithm for forming an independent set in H. An independent
set is...
Operator theory and function theory in Drury-Arveson space and its
quotients
August 5, 2013
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Mathematics
Functional Analysis
Complex Variables
Operator Algebras
Functional Analysis
Complex Variables
Operator Algebras
The Drury-Arveson space Hd2, also known as symmetric Fock space or the
d-shift space, is a Hilbert function space that has a natural d-tuple of
operators acting on it, which gives it the structure of a Hilbert module. This
survey ai...
Hidden-anisotropy-induced π phase shift in all-optical magnetization
precession
August 5, 2013
Physics
Mesoscale and Nanoscale Physics
Materials Science
Laser-induced magnetization precession of an in-plane magnetized Pt/Co/Pt
film with perpendicular interface anisotropy was studied using time resolved
magneto-optical Kerr effect. An additional π shift in the phase of
precession is need...
The convergence Newton polygon of a p-adic differential equation III :
global decompositions
August 4, 2013
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Mathematics
Number Theory
We deal with locally free OX-modules with connection over a
Berkovich curve X. As a main result we prove local and global decomposition
theorems of such objects by the radii of convergence of their solutions. We
also derive a...
Current Algebras from DG Symplectic Pairs in Supergeometry
August 1, 2013
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Physics
Mathematics
Mathematical Physics
High Energy Physics - Theory
Mathematical Physics
Symplectic Geometry
Mathematical Physics
High Energy Physics - Theory
Mathematical Physics
Symplectic Geometry
We propose a new unified formulation of the current algebra theory in terms
of supergeometry. We take a QP-structure, i.e. a differential graded symplectic
structure, on a graded cotangent bundle as a fundamental framework. A Poisson
bracke...
Classification of quasi-affine Generalized Dynkin Diagrams with Rank 4
July 25, 2013
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Mathematics
Quantum Algebra
Quantum Algebra
All quasi-affine connected Generalized Dynkin Diagram with rank =4 are
found. All quasi-affine Nichols (Lie braided) algebras with rank 4 are also
found....
A new graph-based two-sample test for multivariate and object data
July 24, 2013
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Statistics
Methodology
Methodology
Two-sample tests for multivariate data and especially for non-Euclidean data
are not well explored. This paper presents a novel test statistic based on a
similarity graph constructed on the pooled observations from the two samples.
It can b...